*2.1.1. Hybrid method of steepest descent – conjugate gradient with simulated annealing*

X-ray crystallography finds the X-ray final structure of a protein, which usually need refinements using a simulated annealing protocol in order to produce a better structure. Thus, it is very amenable to use simulated annealing (SA) to format the models constructed. Zhang (2011a, 2011d) presents a hybrid method of global search SA with local steepest descent (SD), conjugate gradient (CG) searches. The hybrid method is executed with the following three procedures. (1) Firstly the SD method and then the CG method are executed. These two local search methods are traditional optimization methods. The former has nice convergence but is slow when close to minimums. The latter is efficient but its gradient RMS and GMAX gradient (Case et al., 2010) do not have a good convergence. (2) When models cannot be optimized further, we employ standard SA global search procedure. (3) Lastly, the SD and CG methods are used to refine the models. The PDB (Berman et al., 2000) templates used in (Zhang, 2011a, 2011d) are 2OKZ.pdb, 2ONW.pdb, 2OLX.pdb, 2OMQ.pdb, 2ON9.pdb, 2ONV.pdb, 2ONA.pdb, 1XYO.pdb, 2OL9.pdb, 2OMN.pdb, 2ONX.pdb, 2OMP.pdb, 1YJP.pdb of (Sawaya et al., 2007), but only the 2OMP and 1YJP template-based three MM-Models (Fig. 6a~6c in (Zhang, 2011a)) are successfully passed through the SDCG-SA-SDCG computational procedures.

#### *2.1.2. Hybrid method of discrete gradient with simulated annealing*

Zhang et al. (2011a, 2011d) used 3FVA.pdb as the pdb template to build two MM-Models (Figs. 11~12 in (Zhang et al., 2011a)). The Models were built using a hybrid SA Discrete Gradient (DG (Bagirov et al., 2008)) method. Then the Models were optimized using SDCG-SA-SDCG methods as in (Zhang, 2011a).

### *2.1.3. Computational method of canonical dual global optimization theory*

Zhang et al. (2011, 2011d) used 3NHC.pdb, 3NVF/G/H/E.pdb templates to build several MM-Models (Figs. 9~11 in (Zhang et al., 2011b), and Figs. 5~8 in (Zhang, 2011b)). These Models were built in the use of canonical dual global optimization theory (Gao et al., 2012; Gao and Wu, 2012; Gao, 2000) and then refined by SDCG-SA-SDCG methods as in (Zhang, 2011a).

## **2.2. New material and method, and new MM-models**

### *2.2.1 New material*

This Chapter uses a suitable pdb file template 3NHD.pdb (the GYVLGS segment 127-132 from human prion with V129 (Apostol et al., 2010) from the Protein Data Bank to build MMmodels of AGAAAAGA amyloid fibrils for prions.
